67.12.2 problem 19.1 (b)

Internal problem ID [16641]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.1 (b)
Date solved : Thursday, October 02, 2025 at 01:37:19 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+4*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 x +c_3 \sin \left (2 x \right )+c_4 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 60.014 (sec). Leaf size: 44

ode=D[y[x],{x,4}]+4*D[y[x],{x,2}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\int _1^{K[2]}(c_1 \cos (2 K[1])+c_2 \sin (2 K[1]))dK[1]dK[2]+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.030 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} \sin {\left (2 x \right )} + C_{4} \cos {\left (2 x \right )} \]